Amplification and Feedback ESS205 Spring 2004

How stable should frequency be as voltage is changed? LM555 datasheet – 0.3% per volt, typical

Frequency stability vs. voltage Actual components have many non-ideal characteristics Temperature coefficients, voltage coefficients, memory effects, drift… Specifications matter! Disk ceramic Monolithic Mylar film

555 lab followup Stability of oscillation frequency as power supply voltage is varied Erratic measurement of frequency with multimeters

Frequency Meters Need AC voltage > 250 mV RMS to determine frequency Some show sensitivity to voltage “spikes” Putting resistor in series with meter improves performance – low pass filter effect Bad reading Good reading

Amplifiers Make a signal (voltage or current) bigger Voltage amplifier: Voltage out = Voltage in x G (gain) Small signals: Sensor outputs, radio reception, microelectronics Big signals: Provide mechanical energy (motors, speakers), radio transmission, heating

The ideal amplifier G Vin Vout = G x Vin

Amplification devices Mechanism in which a small signal controls a large signal Water analogy: turning the faucet (small signal) controls large flow of water (big signal)

Vacuum tubes Electrons “boil” off of heated cathode Voltage on grid(s) control current reaching anode Anode Cathode Heater electrons

Transistor Invented 1947 Made of semiconductors – silicon, germanium, gallium arsenide Layered structure – creates junctions The first transistor – Bell Labs, 1947

Transistors Voltage between base and emitter controls current between collector and emitter Types: bipolar (NPN, PNP), JFET, MOSFET ~ 1 mm

Approximate transistor behavior – the Ebers-Moll equations Explicit temperature dependence Parameters (aF, aR, IES, ICS) dependent upon manufacturing details, temperature, etc.

Simple device – complicated behavior The physical laws which describe electronic behavior are not simple Want to make electronic components “act” simple to make them easier to apply Need to build a complicated device to get simple behavior!

How to make electronics “act” simple? Emphasize use of components which have close to ideal behavior Resistors, capacitors Use circuits which are inherently self-compensating for nonideal behavior Ex: voltage divider

Modern operational amplifiers ~ 1 mm LT1006 LMH6642

What’s a good “building block” for amplification? One option: Fixed gains (10, 100, etc) Instrumentation amplifier Another option: Make G…really big, then “throw away” gain you don’t need G Vin Vout = G x Vin

Operational amplifiers V+ Vout=G x (V+-V-) V- G very large (AD820: G ~= 1 million (DC, low load)) Inputs draw little current (AD820: ~10 pA)

Feedback amplifier Feedback: output “feeds back” to input Op amps are always used with feedback How does this work? G Noninverting Feedback Amplifier

Rationale for use of feedback amplifiers Amplifier performance is dictated largely by the behavior of simple passive components (e.g. resistors, capacitors) Pioneers: H. S. Black, H. Nyquist, H. W. Bode, Ball Laboratories, 1920’s “Black’s patent application was delayed for more than nine years in part because the concept was so contrary to established beliefs that the Patent Office initially did not believe it would work. They treated the application in the same manner as one for a perpetual motion machine.” -- W. M. Siebert, Signals and Systems

Basic op amp configurations Noninverting Inverting

Quick analysis of op amp circuits Because G is so large, the difference between V+ and V- must be very small To a good approximation V+=V- Ex: V- is the output of a voltage divider: V- = Vout * R2/(R1+R2). V+ = V-, so Vout = V+ (R1+R2)/R2.

Other op amp configurations Endless variety of circuits for performing different functions: filtering (high pass, low pass, band pass, band reject), integration, differentiation, calculating logarithms, square roots, etc. Use different feedback components and interconnections Ex: Sallen-key lowpass filter

Buffer amplifier Gain of 1 – why use it at all?

Output impedance Ideal voltage source: Voltage independent of load Real voltage source: Acts like an ideal voltage source in series with a resistor Small resistance = “low output impedance” Ideal Real

Ex: Voltage divider No buffer amplifier: Vout depends on RL With buffer amplifier: Vout Independent of RL

Buffer amplifier – gain of 1 Buffer amplifier decreases the output impedance of a signal Makes it easier to transmit signals between parts of a circuit – enables modular construction

Op amp packaging Generally 1, 2, or 4 to a package Standard pinouts Single Dual Quad

Other op amp parameters Speed (slew rate, bandwidth) – what type of signal can be amplified DC, audio, video Precision (input offset voltage) – how closely does the op amp equalize its inputs Power (supply current, output current) – how much power does the amplifier require, and how much power can it deliver to a load

Input and output range Op amp can only amplify signals within a range set by its power supply – can limit applications “Single supply” op amps have input and output voltage range extending to the negative supply Dual supply Single supply